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    Re: Silicon Sea Leg 72
    From: Dan Hogan
    Date: 2001 May 29, 18:35 EDT

    On 29 May 2001, at 15:13, Noyce, Bill wrote:
    > > > > 4)  What is the Compass Course(CC)/Course-to-Steer for Aruba Gap
    > > > >     from the DR position?
    > > > > --  ------------------------------------------------------------
    > > >
    > > > Using Law of Sines, I find I need to adjust my course North
    > > > about 1.5 degrees.
    > > >   CC = 283.4 + 1.5 + 9 = 293.9d
    > >
    > > Mmmm..Barely OK. Try a current vector diagram.
    > I drew a diagram to get the orientation of the pieces right, but I
    > have a hard time measuring the resulting course adjustment, because
    > it's so small.  Thus the attempt at a 'digital' method.
    You can make the vector diagram any convenient size.
    > TC=283.4, Set=265.0, angle between = 18.4 degrees
    >   sin 18.4 / speed = sin adj / drift
    >   sin 18.4 / 8.5 = sin adj / 0.7
    > I did this with log tables before; doing it on the computer now
    > says adj = 1.490 degrees.  The diagram indicates it needs to be
    > added to the course.  Is there something inherantly wrong with
    > this approach, or have I made a slip somewhere?
    Not being mathematically oriented I can't say, but in Shufeldts's The
    Calculator Afloat, he gives the following formulas:
      Finding correction angle and speed of advance
            Value of correction angle
                    sin B = a x sin A /c
        Calculate speed of advance
                    c = a x sin [d -(A + B)] /sin A
      Current Sailing when when track and speed of advance are specified
            Value of correction angle
                    tan B = b x sin A / a - b x cos A
            Value of speed to steam
                    a = b x sin A /sin B
    > > >
    > > > Mid-latitude using 13d 42'
    > > > dLat = 15' N  dLon = 183d W  dep = 177.8 W
    > > > TC = 274.6d  dist = 178.3 nm
    > >
    > > OK. Be aware that above 500 miles at 90d/270d Mid-Latitude can give an
    > error.
    > > Above 1200 mils it gets unreliable.
    > I saw a discussion initiated by Sam Chan about Mercator sailing
    > near 90 or 270, where the problem arises from rounding the course
    > before using dLat/cos(C) to compute the total distance.  Is this
    > a similar problem?  In Mid-Latitude sailing, where we already
    > have dLat and departure, the total distance can be computed either
    > as dLat/cos(C) or as departure/sin(C), so we don't have to divide
    > by a tiny rounded number.
    > Or are you talking about the error in distance that arises from
    > assuming a spherical earth?  What method would be
    > better? I assumed we weren't planning to sail a great-circle
    > course here.
    As I understand it it's caused by the formulas and the how they are derived.
    Mid-Latitude gets error prone when you cross the sperical quadrants. Try
    calculating using Mid-Latitude from North America to Australia and one N.AS.
    to South America of about equal distance.
    GC course comes after the Panama Canal transit ;^)
    Dan Hogan WA6PBY
    Nav-L Web Page: http://www.wa6pby.com
    Catalina 27 "GACHA"

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